Mid Term Review Bybee & Holloway 7 th Grade Math Fall 2011

What Will It Look Like? O Covers Chapters 1-6 O Multiple Choice (scan sheet) O 60 Questions O 90 Minutes O No Calculator O Based on the textbook (like all other tests)

How Do I Study? O Complete the Mid Term Review Test provided O Review old notes O Study old tests O Memorize rules/formulas O Make notecards with vocabulary O DO PRACTICE PROBLEMS!!!! O Find the areas where you struggled the most and focus there first. O Take practice tests with the online textbook.

Chapter 1: Expressions and Patterns O Powers and Exponents O Numerical Expressions O Algebraic Expressions O Properties O Sequences O Square Roots O Cube Roots

Powers and Exponents O Base O Exponent O Factor O Exponential Form/ Standard Form O Be able to evaluate powers p. 27 #18-24 even

Numerical Expressions O Order of Operations!!!! O PEMDAS p. 31 #20-26 even

Algebraic Expressions O Variables O Coefficients O PLUG IT IN, PLUG IT IN!!!! O Write an expression when given a situation p. 36 #8, even

Properties O Commutative O Associative O Identity O DISTRIBUTIVE!!!!!! (focus here) O “Justify each step”; know how to use each O FOLDABLE p. 40 #14-22 even

Sequences O Sequence O Term O Arithmetic Sequence O Geometric Sequence O Be able to “Extend” any sequence by seeing the pattern p. 47 #10-16 even

Squares & Square Roots O Square O Square Root O Cube Root O Radical Sign O FOLDABLE O Be able to find a SQUARE of a number and also a SQUARE ROOT or CUBE ROOT of a number p. 55 #14-24 even

Chapter 2: Integers O Absolute Value O Coordinate Plane O Adding Integers O Subtracting Integers O Multiplying and Dividing Integers

Absolute Value O Integer O Absolute Value O Number Line O Be able to evaluate expressions with absolute value p. 79 #14-18 even #28-32 even

Coordinate Plane O Origin O x-axis, y-axis/ x-coordinate, y-coordinate O Four Quadrants O Ordered Pairs O Know how to plot points & identify the quadrant p. 84 #10-18 even

Add & Subtract Integers ADDITION: Same signs, add and keep Different signs subtract Take the sign of the larger number Then, you’ll be exact! SUBTRACTION: LEAVE, CHANGE, CHANGE/ADD THE OPPOSITE p. 91 #20-28 even p. 97 #22-28 even

Multiply & Divide Integers O Same Signs- POSITIVE O Different Signs- NEGATIVE O Pay attention to when you have exponents p. 107 #20-28 even p. 112 #24-30 even

Chapter 3: Rational Numbers O Terminating and Repeating Decimals O Comparing & Ordering Rational Numbers O Add & Subtract Like Fractions O Add & Subtract Unlike Fractions O Add & Subtract Mixed Numbers O Multiply Fractions O Divide Fractions O Multiply & Divide Monomials O Negative Exponents O Scientific Notation

Terminating & Repeating Decimals O Changing Fraction into a Decimal using division O Sometimes the answers terminate and other times they repeat O Bar Notation is used to show repeating p. 131 #22-28 even

Compare & Order Rational Numbers O Rational Numbers (be aware of what they are) O Comparing Fractions & Decimals using, = O Might need Common Denominators before you can compare O Might need to change the Fraction to Decimal before you can compare p. 136 #14-20 even

Add & Subtract Fractions 1. Must have a COMMON DENOMINATOR 2. Add the numerator 3. Keep the denominator 4. Simplify O BE CAREFUL WITH THE NEGATIVES!!!!! O All Integer Rules apply here p. 142 #14-20 even p. 149 #20-28 even

Add & Subtract Mixed Numbers 1. Add or subtract the fraction 2. You might need to rename using the LCD 3. Add or subtract the whole numbers 4. Simplify OR 1. Change to improper fractions 2. Get a common denominator 3. Add or Subtract 4. Simplify p. 155 #14-24 even

Multiply Fractions 1. Change any Mixed # to Improper Fraction 2. Multiply the numerators 3. Multiply the denominators 4. Simplify O YOU DO NOT NEED COMMON DENOMINATORS! O Pay attention to those negatives p. 163 #14-20 even

Divide Fractions O You will have to change any Mixed # to an Improper Fraction O LEAVE, CHANGE, FLIP or… O Multiply by the reciprocal O Apply the same rules as Multiplying Fractions p. 171 #22-28 even

Multiply & Divide Monomials O To multiply powers with the same base, add the exponents (Product of Powers) O To divide powers with the same base, subtract the exponents (Quotient of Powers) O You can always write it out in expanded form to help yourself! p. 179 #20-34 even

Negative Exponents p. 183 #22-40 even Look at the textbook here to review. Rewrite using positive and negative exponents

Scientific Notation O Writing really big numbers or really small numbers in a manageable way O Standard Form (1,457,000) O Scientific Notation (1.457 x 10 6 ) O Know which way to move the decimal when using positive or negative exponents p. 187 #18-28 even

Chapter 4: Equations and Inequalities O Solve One-Step Addition and Subtraction Equations O Solve One-Step Multiplication and Division Equations O Solve Equations with Rational Coefficients O Solve Two-Step Equations O Solve Equations with Variables on Both Sides O Solve Inequalities by Addition or Subtraction O Solve Inequalities by Multiplication or Division

Solve One-Step Addition and Subtraction Equations 1. What’s your variable? 2. What happened to your variable? 3. How do you un-do that? O Do the opposite operation O Remember: be careful when given negatives p. 211 #12-20 even

Solve One-Step Multiplication and Division Equations 1. What’s your variable? 2. What happened to your variable? 3. How do you un-do that? O Do the opposite operations O Remember the Integer Rules from Chapter 2 p. 218 #16-22 even

Solve Equations with Rational Coefficients O Multiplicative Inverse/ Reciprocal If there’s a fraction before a variable, You gotta multiply it by the reciprocal! O If there is a decimal before a variable, divide both sides by that decimal. p. 224 #22-32 even

Solve Two-Step Equations O Undo the operations in the REVERSE order of the Order of Operations 1. Undo any addition and subtraction 2. Undo any multiplication and division O You are working to isolate the variable O Just remember the rules for the one-steps and remember the integer rules p. 233 #12-20 even

Solve Equations with Variables on Both Sides 1. Combine all variables to one side of the equation using addition or subtraction 2. Combine all numbers to the other side of the equation using addition or subtraction 3. Use multiplication or division to isolate the variable O This is called “COMBINING LIKE TERMS” p. 238 #20-28 even

Solve Inequalities by Addition or Subtraction O Solve the same way as one-step equations O The symbol will be >, <, ≤, ≥ O Solutions can be graphed on a number line where have an open circle and, ≤, ≥ use closed circles p. 247 #18-26 even

Solve Inequalities by Multiplication or Division Song!: Only if you MULTIPLY by a negative number (negative number) Only if you DIVIDE by a negative number (negative number) You switch the inequality, You switch the inequality, You switch the inequality p. 252 #18-28 even

Chapter 5: Proportions and Similarity O Rates/ Unit Rates O Proportional and Nonproportional Relationships O Solve Proportions O Scale Drawings O Similar Figures O Perimeter and Area of Similar Figures

Rates/ Unit Rates O Ratio (comparing 2 numbers) O Rate (comparing with units) O Unit Rate (comparing a number to 1) O Be able to find the best deal! p. 269 #12-16 even

Proportional & Nonproportional Relationships O Proportional: have a constant ratio O Nonproportional: do not have a constant ratio O Simplifying of ratios O Tables p. 274 #5-8 all

Solve Proportions O Two equivalent ratios O A variable in one of the four “positions” O Use cross multiplication to solve O Be able to WRITE a proportion AND solve it p. 279 #10-20 even

Scale Drawings O Scale Drawings O Scale Model O Scale O Scale Factor O Be able to use a scale within a proportion to find the missing measurement of something p. 287 #2-7 even

Similar Figures O Figures that have the same shape but NOT the same size O Be able to find the missing measurement of a figure by finding the scale O Use a proportion to solve p. 297 #5-10 all

Perimeter and Area of Similar Figures O Perimeter- if two figures are similar, you can multiply the original perimeter by the scale factor to get the new perimeter O New P = Old P (scale factor) O Area- if two figures are similar, you can multiply the original area by the scale factor SQUARED to get the new area O New A = Old A (scale factor) 2 p. 301 #5-10 all Look at the Pencast on these questions.

Chapter 6: Percent O Percent of a Number O Percent and Estimation O Percent Proportion O Percent Equation O Percent of Change O Sales Tax, Tip, Discount O Simple Interest

Percent of a Number O Find the percent of the number two possible ways: 1. Write the percent as a fraction then multiply 2. Write the percent as a decimal then multiply O Be careful when you have decimals or fractions WITHIN the percentage: 6.25% = AND 0.25% = p. 322 #24-30 even

Percent and Estimation O Round numbers BEFORE you do the multiplication. O Find “compatible numbers”…numbers that are easy to multiply in your head. O Change numbers like 23% to 25% or 789 to 800 p. 328 #23-28 all

The Percent Proportion O Using a proportion to find a PERCENT, a PART, or a WHOLE O Look at your FOLDABLE O Part – IS O Whole- OF p. 335 #8-16 even

The Percent Equation O Using an equation to find the PERCENT, PART, or WHOLE O part = percent (whole) O Part – IS O Whole – OF p. 340 #14-22 even

Percent of Change O Finding a percent of increase or a percent of decrease O Write a ratio/fraction O Numerator is the difference in the numbers O Denominator is the original amount O Once you have your ratio, divide and get a decimal. Change that decimal to a percentage p. 297 #5-10 all

Sales Tax, Tip, Discount O Find the percentage of the price by solving a multiplication problem O Basically multiply the price by the percent (in decimal form) O Add or subtract to the original price to find the final price p. 353 #10-14 all p. 357 #6-12 even

Simple Interest O Principal O Rate O Interest O I = prt O Plug it in, Plug it in (and multiply) O Make sure you change all the percentages and months to decimals p. 361 #8-16 even